The present invention relates generally to systems and methods for processing Polymerase Chain Reaction (PCR) data, and more particularly to systems and methods for determining characteristic cycle threshold (Ct) or elbow values in PCR amplification curves, or elbow values in other growth curves, that have a parabolic shape.
The Polymerase Chain Reaction is an in vitro method for enzymatically synthesizing or amplifying defined nucleic acid sequences. The reaction typically uses two oligonucleotide primers that hybridize to opposite strands and flank a template or target DNA sequence that is to be amplified. Elongation of the primers is catalyzed by a heat-stable DNA polymerase. A repetitive series of cycles involving template denaturation, primer annealing, and extension of the annealed primers by the polymerase results in an exponential accumulation of a specific DNA fragment. Fluorescent probes or markers are typically used in the process to facilitate detection and quantification of the amplification process.
A typical real-time PCR curve is shown in FIG. 1 (solid line), where fluorescence intensity values are plotted vs. cycle number for a typical PCR process. In this case, the formation of PCR products is monitored in each cycle of the PCR process. The amplification is usually measured in thermocyclers which include components and devices for measuring fluorescence signals during the amplification reaction. An example of such a thermocycler is the Roche Diagnostics LightCycler (Cat. No. 20110468). The amplification products are, for example, detected by means of fluorescent labelled hybridization probes which only emit fluorescence signals when they are bound to the target nucleic acid or in certain cases also by means of fluorescent dyes that bind to double-stranded DNA.
For a typical PCR curve, identifying a transition point at the end of the baseline region, which is referred to commonly as the elbow value or cycle threshold (Ct) value, is extremely useful for understanding characteristics of the PCR amplification process. The Ct value may be used as a measure of efficiency of the PCR process. For example, typically a defined signal threshold is determined for all reactions to be analyzed and the number of cycles (Ct) required to reach this threshold value is determined for the target nucleic acid as well as for reference nucleic acids such as a standard or housekeeping gene. The absolute or relative copy numbers of the target molecule can be determined on the basis of the Ct values obtained for the target nucleic acid and the reference nucleic acid (Gibson et al., Genome Research 6:995-1001; Bieche et al., Cancer Research 59:2759-2765, 1999; WO 97/46707; WO 97/46712; WO 97/46714). The elbow value in region 20 at the end of the baseline region 15 in FIG. 1 would be in the region of cycle number 36.
The determination of elbows (or cycle thresholds, Ct) for PCR curves is needed for quantitative analysis of real-time PCR (RT-PCR). Many algorithms have been developed for this use, e.g., based on intersection of a normalized data curve with a threshold or by determining the maximum curvature or 2nd derivative, either analytically (e.g., using a curvature algorithm) or numerically, on a normalized data curve, as described in U.S. application Ser. No. 11/316,315, filed Dec. 20, 2005; U.S. application Ser. No. 11/349,550, filed Feb. 6, 2006; U.S. application Ser. No. 11/458,644, filed Jul. 19, 2006; U.S. application Ser. No. 11/533,291, filed Sep. 19, 2006; U.S. application Ser. No. 11/861,188, filed Sep. 25, 2007; U.S. application Ser. No. 12/209,912, filed Sep. 12, 2008 (“ELCA Algorithm”), the disclosures of which are each hereby incorporated by reference for all purposes. These methods work exceedingly well provided that the underlying curve approximates a sigmoid shape. In the rare occasion when the raw data curve has a parabolic shape, then the elbow value as determined by these methods will typically result in an elbow value that is larger than one would expect by examination of the data curve.
Consider the real-time PCR (RT-PCR) curves from a West Nile Virus (WNV) assay shown in FIG. 1. The solid black curve has a typical sigmoidal shape, which is amendable to analysis with algorithms developed previously. The dashed curve, however, resembles a parabolic curve and lacks a plateau region. The elbow values of the two curves shown in FIG. 1 have the values given in Table 1 below, when analyzed by the ELCA Algorithm as an example. The ELCA Algorithm numerically determines the elbow value as the point of maximum in the curvature or second derivative.
TABLE 1Ct values for Sigmoidal and Parabolic CurvesELCA CtSolid Curve35.46Dashed Curve45.43
The elbow value for the solid curve is consistent with the value one would normally assign to a sigmoid curve, whereas a vertical line drawn at the elbow value for the parabolic dashed curve intersects the dashed curve at a value significantly higher than one would typically assign to this curve.
Accordingly, it is desirable to develop systems and methods to deal with these type of curves, and also to identify when such a parabolic curve is present.